Large deviation principle of occupation measure for stochastic real Ginzburg-Landau equation driven by $\alpha$-stable noises

TL;DR

This paper proves a large deviation principle for the occupation measure of a stochastic Ginzburg-Landau equation driven by heavy-tailed $ extalpha$-stable noises, revealing a new phenomenon where dissipation overcomes noise effects.

Contribution

It introduces a novel large deviation result for the occupation measure of the stochastic Ginzburg-Landau equation with $ extalpha$-stable noises, using a hyper-exponential recurrence criterion.

Findings

Strong dissipation can dominate heavy-tailed noise effects

The large deviation principle is established for the occupation measure

A new phenomenon of dissipation overcoming noise is reported

Abstract

We establish a large deviation principle for the occupation measure of the stochastic real Ginzburg-Landau equation driven by $\alpha$-stable noises. The proof is based on a hyper-exponential recurrence criterion. Our result indicates a phenomenon that strong dissipation beats heavy tailed noises to produce a large deviation, it seems to us that this phenomenon has not been reported in the known literatures.